where \(r^2=(x-\pi )^2+(z-\pi )^2\) , the parameters are set to \(c_r=0.7\)  and \(c_y=0.6\) , and the amplitude of the perturbation was scaled to have an energy-norm of \(10^{-5}\)  to ensure that the effect of nonlinearity is negligible. This initial condition, which was first studied in [1]} and also in [2]}, is a model of a disturbance that could be generated in experiments using a spanwise and streamwise periodic array of axisymmetric jets injecting fluid perpendicular to the wall. The dataset obtained from this simulation is then comprised of a sequence of 300 snapshots of the three-dimensional velocity-perturbation field recorded every \(0.5\)  time units.
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